AS recently (23 January) changed its lowest level awards to 20K on the SAN-OGG route. If you search on alaskaair.com for a 'use miles' ticket, you can see that the nonstop flight is showing availability at the 20K level for some of your dates - however I'm unsure if this still maps over to BA availability. Best thing to do is to search alaskaair.com to see if you see any available dates for four, and then call BA to see if they can also see the flights.

If they are available through BAEC, as the flight is 2536 miles, the Avios cost should be 12,500 miles plus a few dollars in taxes. I've had BA waive the telephone booking fee for an AS award, but YMMV.